竞争风险场合PL型估计的弱一致收敛性

本文构造了竞争风险场合分布函数的乘积极限（PL）型估计，运用经验过程的逼近理论及Taylor展开方法，给出了PL型估计在全直线上的弱一致收敛速度及其充分必要条件。     

相依竞争风险场合下生存函数的广义自相合估计

近些年来,生存函数的非参数估计问题受到了很大的关注.首先,Kaplan 和 Meier(1958)提出了乘积限(product limit)估计,并且证明这种估计实际上也是极大似然估计.而后 Breslow 和 Crowley(1974)、F(?)ldes 和 Rejt(?)(1981)在特定的删失机制和某些连续性假定下探讨了 PL 估计(即乘积限估计)的一些基本性质.Langberg,Proschan 及Quinzi(1981)在相依竞争风险场合下进一步推广了 PL 估计,并证明了 PL 估计是强相合的.Tsai(1986)推广了 Efron 定义的自相合性,在一个风险及—个删失变量的场     

随机截断下PL估计的强表示式

本文在随机左截断情形下,研究了分布函数不连续时,分布函数的乘积限估计（PL估计）Fn(x）的一致强表示式,得到与分布函数连续情形下相同的结果。     

复空间的PL凸性与解析鞅不等式

该文研究了取值于复拟Banach空间的解析鞅不等式与该空间的PL—致凸性的关系，证明了解析鞅的q均方函数的弱（1，1）型，强（p，p）型和凸Φ中函数不等式，并应用它们给出了复空间的q—致PL可凸性的等价条件，同时借助解析鞅q均方函数的增长速度给出了同样的刻划．     

NA列递归密度核估计的相合性

本文在一定的条件下证明了基于NA样本序列的递归型密度核估计的均方相合性和逐点强相合性，作为在可靠性问题中的应用，利用NA样本构造了生存函数和失效率函数的估计，并讨论了相应的逐点强相合性。     

Stein流形上α_b的Hlder和L~p估计(英文)

本文得到了Ｓｔｅｉｎ流形强拟凸域上（ｐ，ｑ）型ｂ—方程解的Ｈｌｄｅｒ和Ｌｐ估计     

一类简化的Pickands型估计

本文研究了一类简化的Ｐｉｃｋａｎｄｓ型估计的相合性，渐近正态性和强收敛速度。     

Pickands型估计的推广

本文把Ｐｉｃｋａｎｄｓ型估计推广到更一般情形，证明了它的相合性，强收敛速度．     

二元竞争风险场合二元PL估计的弱收敛性及其Bootstrap结果

本文考虑了在二元竞争风险场合下二元PL估计的问题.文中给出了关于二元PL估计的独立同分布表达式,即将估计的差表为均值为零的独立同分布过程的和,且其余项的阶为O((u^-1logn)^3/4)a.s.,并证明该过程弱收敛到一个二元Gauss过程.关于Bootstrap情况也得到了类似的结果.     

Stein流形上θ↑—b的Holder和L^v估计

本文得到了Ｓｔｅｉｎ流形强拟凸域上（ｐ，ｑ）型θ↑－ｂ－方程解的Ｈｏｌｄｅｒ和Ｌ＾ｐ估计。     

球面数据核近邻估计的强相合性

该文绘出了球面数据密度函数的核近邻估计,通过对核估计与近邻估计相互关系的讨论,建立了核近邻估计的逐点强相合性及一致强相合性．     

Improvements of the Maximum Pseudo-Likelihood Estimators in Various Spatial Statistical Models

Abstract

Maximum pseudo-likelihood estimation has hitherto been viewed as a practical but flawed alternative to maximum likelihood estimation, necessary because the maximum likelihood estimator is too hard to compute, but flawed because of its inefficiency when the spatial interactions are strong. We demonstrate that a single Newton-Raphson step starting from the maximum pseudo-likelihood estimator produces an estimator which is close to the maximum likelihood estimator in terms of its actual value, attained likelihood, and efficiency, even in the presence of strong interactions. This hybrid technique greatly increases the practical applicability of pseudo-likelihood-based estimation. Additionally, in the case of the spatial point processes, we propose a proper maximum pseudo-likelihood estimator which is different from the conventional one. The proper maximum pseudo-likelihood estimator clearly shows better performance than the conventional one does when the spatial interactions are strong.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.     

Conditional Quantile Estimation with Truncated, Censored and Dependent Data

This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.     

分位点函数的光滑非参数估计的BAHADUR表示

文中对分位函数给出了具有更广泛应用的光滑分位估计,证明了该光滑分位估计的逐点和一致的Bahadur强表示定理;并由此结果推导了估计的重对数律,强逼近等深刻结果。     

SOME RESULTS ON ESTIMATION OF THE TAIL INDEX OF A DISTRIBUTION

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＳｕｐｐｏｓｅｔｈａｔＦｉｓａｄｉｓｔｒｉｂｕｔｉｏｎｆｕｎｃｔｉｏｎｓｕｃｈｔｈａｔ,ｆｏｒａｎｙｘ＞０,ｌｉｍｔ→∞１－Ｆ（ｔｘ）１－Ｆ（ｔ）＝ｘ－１γ,γ＞０．（１．１）ＷｅｃａｌγｔｈｅｔａｉｌｉｎｄｅｘｏｆＦ．...     

随机左截断数据下乘积限估计的强逼近及其应用

本文建立了左截断数据下乘积限估计的强表示结果,其误差项的收敛速度达到重对数律。作为应用,推出了乘积限估计的重对数律和强逼近等深刻结果。     

Strong Consistency of $M$ Estimator in Linear Model for $\widetilde{φ}$-Mixing Samples

The strong consistency of $M$ estimator of regression parameter in linear model for $\widetilde{φ}$-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of $M$ estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.     

Estimation of a tail index based on minimum density power divergence

In this paper, we consider the minimum density power divergence estimator for the tail index of heavy tailed distributions in strong mixing processes. It is shown that the estimator is consistent and asymptotically normal under regularity conditions. The simulation results demonstrate that the estimator is robust in the presence of outliers.